I am an Engineer, but a Mechanical one, so I would like to know your opinion about what I believe makes Bose speakers popular.
In a perfect world, accurate (High Fidelity) sound reproduction would mean, as you have stated, making the sound system "disappear" leaving only the illusion of a live performance with live, actual, physical instruments and performers. That concept works for acoustic instruments but the sound of electronic ones will always be colored by the electronics and speakers that make them work, so electronic instruments have no actual "real" sound, unless you consider "real" whatever signal is fed the Amplifier. So, accurate sound reproduction means accurately capturing said sound, storing it and reproducing it, usually by means of paper cones with precious little resemblance to wood resonance chambers, vibrating strings, metal tubes or discs, and flat, tense leather membranes (maybe what speakers resemble the most are drums). The issue here is that a "good" "High Fidelity" system will (at least in theory) accurately reproduce whatever it is fed, so it must be fed an extremely high-quality signal in order for it to produce high-quality sound. The worse the input signal is, the more its undesirable effects will be exacerbated by a high-quality system. As a result, a poor input signal will sound worse the better the system it is fed into is.
On the other hand, as far as I understand, what Bose does is process the input signal to get rid of any perceivable negative artifacts (by means of psychoacoustics) and "adapt" it to whatever their hardware is capable of doing best and the listener's ears and brain feel "comfortable" with. In other words, Bose will not ask of neither the input signal, nor the speaker, nor the listener, something they are not capable of doing reasonably well. That may definitely not be "High Fidelity", but the effect is that, in my experience, Bose speakers always sound just "as well" regardless of the input signal they are being fed, and they are not tiring to listen to. One can listen to them all day long using any practically any source material imaginable, and never grow tired or end up with a headache or ringing ears, something that cannot always be said of high-end equipment. Plus, they're much more practical to carry around than huge speakers with 15-inch drivers and welding-plant amplifiers. They may be inaccurate, but simply more practical in most real-world scenarios. And it's all about perception. Don't you agree?